Haar Systems on Equivalent Groupoids

TL;DR

This paper proves that for second countable locally compact Hausdorff groupoids, the existence of a Haar system is maintained under the equivalence relation, ensuring stability of this property across equivalent structures.

Contribution

It establishes that the Haar system property is invariant under groupoid equivalence for a broad class of groupoids.

Findings

Haar systems are preserved under groupoid equivalence.

The result applies to second countable locally compact Hausdorff groupoids.

This invariance aids in understanding the structure of groupoids in analysis.

Abstract

For second countable locally compact Hausdorff groupoids, the property of possessing a Haar system is preserved by equivalence.